Question: Solve for $x$ and $y$ using elimination. ${6x-2y = 12}$ ${5x+3y = 52}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $6$ ${-30x+10y = -60}$ $30x+18y = 312$ Add the top and bottom equations together. $28y = 252$ $\dfrac{28y}{{28}} = \dfrac{252}{{28}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {6x-2y = 12}\thinspace$ to find $x$ ${6x - 2}{(9)}{= 12}$ $6x-18 = 12$ $6x-18{+18} = 12{+18}$ $6x = 30$ $\dfrac{6x}{{6}} = \dfrac{30}{{6}}$ ${x = 5}$ You can also plug ${y = 9}$ into $\thinspace {5x+3y = 52}\thinspace$ and get the same answer for $x$ : ${5x + 3}{(9)}{= 52}$ ${x = 5}$